We can use the point-slope formula to write an equation for this problem. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the slope and the values from the point in the problem gives:
#(y - color(red)(-5)) = color(blue)(-4)(x - color(red)(2))#
#(y + color(red)(5)) = color(blue)(-4)(x - color(red)(2))#
We can also solve for #y# to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.
#y + color(red)(5) = (color(blue)(-4) xx x) - (color(blue)(-4) xx color(red)(2))#
#y + color(red)(5) = -4x - (-8)#
#y + color(red)(5) = -4x + 8#
#y + color(red)(5) - 5 = -4x + 8 - 5#
#y + 0 = -4x + 3#
#y = color(red)(-4)x + color(blue)(3)#
